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Hybrid System Model Identification for Terrestrial Locomotion Dynamics

Developing model reduction and identification tools for hybrid models of terrestrial MAST platforms to enhance understanding of locomotion dynamics. Using scalable algorithms to identify both detailed and reduced models for complex polyped systems. Exploring mathematical approximations and real-time experiments for empirical data validation.

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Hybrid System Model Identification for Terrestrial Locomotion Dynamics

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  1. MCE-2.6 Identification of Stochastic Hybrid System Models Shankar Sastry Sam Burden UC Berkeley

  2. MCE-2.6 Overview Identification of Stochastic Hybrid System Models • Sam Burden • PhD Candidate, UC Berkeley • Advised by Prof. Shankar Sastry • Collaborators: • Prof. Ronald Fearing (MCE, UC Berkeley) • Prof. Robert Full (MCE, UC Berkeley) • Prof. Daniel Goldman (MCE, GATech) • Goal: model reduction and system identification tools for hybrid models of terrestrial MAST platforms • Theorem: reduction of N-DOF polypeds to common 3-DOF model • Algorithm: scalable identification of detailed & reduced models

  3. Technical Relevance:Dynamics of Terrestrial Locomotion OctoRoACH designed by Andrew Pullin, Prof. Ronald Fearing

  4. Technical Relevance:Reduction and Identification of Polyped Dynamics physical system robot, animal system identification polyped models 10—100 DOF model reduction reduced model < 10 DOF

  5. Reduction of Polyped Dynamics physical system robot, animal system identification polyped models 10—100 DOF model reduction reduced model < 10 DOF

  6. Reduction of Polyped Dynamics m l, k, β • Detailed morphology • Multiple limbs • Multiple joints per limb • Mass in every limb segment • Precedence in literature • Multiple massless limbs (Kukillaya et al. 2009) • Realistic disturbances • Fractured terrain (Sponberg and Full 2008) • Granular media (Goldman et al. 2009) M, I M I m l : body mass : moment of inertia : leg mass : leg length k β : leg stiffness : leg damping

  7. Reduction of Polyped Dynamics • Theorem:polypedmodel reduces to 3-DOF model • Let H = (D, F, G, R) be hybrid system with periodic orbit g • Then there exists reduced system (M, G) and embedding • Dynamics of H are approximated by (M, G) • (Burden, Revzen, Sastry2013 (in preparation) )

  8. Identification of Polyped Dynamics physical system robot, animal system identification polyped models 10—100 DOF model reduction reduced model < 10 DOF

  9. Identification of Polyped Dynamics • Mathematical models are necessarily approximations • Model parameters must be identified & validated using empirical data • Identification problem for hybrid system H = (D, F, G, R): • Challenging to solve for terrestrial locomotion: circulating limbs introduce nonlinearities in dynamics & transitions impact of limb with substrate introduces discontinuities in state

  10. Lateral perturbation experiment real-time

  11. Lateral perturbation experiment Platform accelerates laterally at 0.6 ± 0.1 g in a 0.1 sec interval providing a 50 ± 3 cm/sec specific impulse, then maintains velocity. camera diffuser mirror magnetic lock animal motion cart Cockroach running speed: 36 ± 8cm/sec Stride frequency: 12.6 ± 2.9 Hz (~80ms per stride) trackway cart motion pulley rail mass cable elastic ground Revzen, Burden, Moore, Mongeau, & Full, Biol. Cyber. (to appear) 2013

  12. Lateral perturbation experiment Measured: • Heading, body orientation • Linear, rotational velocity • Distal tarsal (foot) position • Cart acceleration induces equal & opposite animal acceleration

  13. Mechanical self-stabilization Animal Lateral Leg Spring (LLS) Schmitt & Holmes 2000 3 legs act as one • Cart acceleration induces equal & opposite animal acceleration • Apply measured acceleration directly to model Quantitative predictions for purely mechanical feedback

  14. Mechanical self-stabilization Animal Lateral Leg Spring (LLS) Schmitt & Holmes 2000 • Apply measured acceleration directly to model • Cart acceleration induces equal & opposite animal acceleration Inertial Disc

  15. Result: LLS Fits Recovery for >100ms Animal Inertial Disc Lateral Leg Spring (LLS)

  16. Technical Accomplishments:Reduction and Identification of Polyped Dynamics physical system robot, animal system identification polyped models 10—100 DOF model reduction reduced model < 10 DOF

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